Normal form analysis of a mean-field inhibitory neuron model

Abstract

In neuroscience one of the open problems is the creation of the alpha rhythm detected
by the electroencephalogram (EEG). One hypothesis is that the alpha rhythm
is created by the inhibitory neurons only. The mesoscopic approach to understand
the brain is the most appropriate to mathematically modelize the EEG records of the
human scalp. In this thesis we use a local, mean-field potential model restricted to
the inhibitory neuron population only to reproduce the alpha rhythm. We perform
extensive bifurcation analysis of the system using AUTO.We use Kuznetsov’s method
that combines the center manifold reduction and normal form theory to analytically
compute the normal form coefficients of the model. The bifurcation diagram is largely
organised around a codimension 3 degenerate Bogdanov-Takens point. Alpha rhythm
oscillations are detected as periodic solutions.